Tracking time assiduously used to be a normal part of RPGs in the 70s and 80s, but it seems to have become a lost skill.
The answer is to actually track the time as it passes in-game. Know how long actions take, and estimate other things in blocks of time. The players have a discussion about strategy? 10 minutes. They travel overland? Mark how many hours that takes. They spend time in a place of business? Well, how long does that usually take in your own life?
To make players aware of the passing time, tell them. "Okay, so ten minutes have passed while you argue about where to go next. Are you decided yet?" then let them keep discussing or not, as they like.
If you don't want to give away the exact "zero hour", then that's all you need do: just keep telling them how much time their actions take. The sudden awareness of time that you are making part of the game will create a sense of time pressure all by itself.
However, if you want to hint that something happens after 13 hours, make a paper clock or straight timeline, marked from 0 to 13, maybe with 1/2 hour increments or whatever is convenient for your own time-keeping, and optionally with an ominous icon above the 13 that makes it clear this is an end and not just the point where you start over with a fresh time sheet. Put this where it's visible to the players, and move a marker or shade in used-up time as you announce time passing, without explaining what this mysterious clock is for. They'll see that they're inching closer to the end, and that will seem ominous.